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I am considering the following ODE \begin{equation} \begin{split} &\frac{d^2}{dy^2}u + \frac{\alpha}{(1+y^2)^{\frac{r}{2}}}u = \delta(y)\\ &\lim_{|y|\to \infty}u(y) = 0. \end{split} \end{...

This question is a cross-post from MSE. it is also a special case of this question. Let $B=\{z\in \mathbb C \,|\,|z|\le 1\}$, and let $f:B \to \mathbb{C}$ be holomorphic on the interior $B^o$, and ...